Higher-order sliding modes, differentiation and output-feedback control
Higher-order sliding modes, differentiation and output-feedback control
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DOI：
10.1080/0020717031000099029
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发表时间：
2003-06-01
影响因子：
2.1
通讯作者：
Levant, A
中科院分区：
文献类型：
--
作者：
Levant, A
滑动模态是动态系统在不连续集上的一种运动，它能精确地保持给定的约束条件，具有理论上无限频率切换的特点。标准滑动模式提供有限时间收敛、精确保持约束以及对内部和外部干扰的鲁棒性。然而，约束的相对程度必须是I，并且可能产生危险的抖动效应。高阶滑模保持或推广了标准滑模的主要性质，并消除了上述限制。与标准滑动模式的一阶相比，r-滑动模式实现相对于采样间隔提供高达r阶的滑动精度。这样的控制器需要高阶实时导数的输出是可用的。通过提出具有有限时间收敛性的任意阶鲁棒精确微分器来实现所需的信息。这些微分器具有最佳渐近输入噪声，并可用于数值微分。所得到的控制器提供了完整的输出反馈实时控制的任何输出变量的不确定动态系统，如果它的相对程度是已知的和常数。计算机仿真结果证实了理论分析的正确性。
Being a motion on a discontinuity set of a dynamic system, sliding mode is used to keep accurately a given constraint and features theoretically-infinite-frequency switching. Standard sliding modes provide for finite-time convergence, precise keeping of the constraint and robustness with respect to internal and external disturbances. Yet the relative degree of the constraint has to be I and a dangerous chattering effect is possible. Higher-order sliding modes preserve or generalize the main properties of the standard sliding mode and remove the above restrictions. r-Sliding mode realization provides for up to the rth order of sliding precision with respect to the sampling interval compared with the first order of the standard sliding mode. Such controllers require higher-order real-time derivatives of the outputs to be available. The lacking information is achieved by means of proposed arbitrary-order robust exact differentiators with finite-time convergence. These differentiators feature optimal asymptotics with respect to input noises and can be used for numerical differentiation as well. The resulting controllers provide for the full output-feedback real-time control of any output variable of an uncertain dynamic system, if its relative degree is known and constant. The theoretical results are confirmed by computer simulation.